M. C. Fitting. The logic of proofs, semantically. Annals of Pure and Applied Logic, v. 132, pp. 1--25, 2005. Home/Search Document Not in Database Summary Related Articles Check |
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Handbook of Set Theory - Foreman Kanamori And (2 citations) (Correct)
....every singular cardinals #, and hence 2 for every singular strong limit cardinal #. Jensen s proof can be generalized to larger cardinals, but the full strength of the failure of the SCH was not discovered until Gitik combined the covering lemma with Shelah s pcf theory: 2. 2 Theorem (Gitik [15,18]) The failure of the singular cardinal hypothesis is equiconsistent with o(#) # . In section 4.3 we prove that the failure of the singular cardinal hypothesis implies that there is an inner model with o(#) # ; chapter gitik gives a proof of the other direction along with a full ....
....of clause (4) which is the end of the proof of theorem 4.19, the covering lemma for sequences of measures. 4.3. The Singular Cardinal Hypothesis We will now use theorem 4.19 to establish the lower bound for the strength of a failure of the singular cardinal hypothesis: 4. 41 Theorem (Gitik [15]) If there is a singular cardinal # with 2 then there is a cardinal # with o(#) in K. The proof combines the use of the covering lemma with two theorems from Shelah s pcf theory. 4.42 Theorem (Shelah [46, Conclusion 5.10(2) on page 410] If # is the least cardinal satisfying ....
, The strength of the failure of the singular cardinal hypothesis, Annals of Pure and Applied Logic 51 (1991), 215--240.
Computability, Definability and Algebraic Structures - Downey (1999) (Correct)
....underlying motivating question was due to Ruzsa who, in the 70 s, asked for a reasonable classi cation of the sets that are di erence sets. In particular, Rubel reformulated the question to ask if the set was Borel. Again computability theory provides a negative answer. Theorem 2. 21 (Schmerl, [107]) The set of di erence sets is 1 complete. Schmerl s paper contains many other good things besides, and is beautifully written. 3 Degrees of Isomorphism Types The natural guess for de nition which assigns a degree to an isomorphism type would be the least degree of any presentation in that ....
Schmerl, J., What's the di erence?, Annals Pure and Applied Logic, Vol. 93 (1998), 255-261.
Proofnets and Context Semantics for the Additives - Mairson, Rival (Correct)
....His syntax involves boxes, but the problems he encounters are related to ours. He proves a restricted confluence property that should be extendable to our settings without any problem. Following our work, we discovered that the notion of multiboxes appears in a manuscript of Tortora De Falco [19]. Our notion of generalized boxes is in the same spirit as his multiboxes; however, we have integrated a reduction preserving semantics akin to Laurent [15] together with a more generalized notion of garbage that preserves the linearity of additive cut elimination. The reasons why we chose to ....
L. Tortora de Falco. The additive multiboxes. Annals of Pure and Applied Logic. To appear.
Tree-interpretable Structures - Blumensath (2001) (Correct)
....O) is tree interpretable. Proof. O is GSO(# ) definable by the preceding lemma. Since A is of finite treewidth it follows that O is even MSO(# ) definable and, therefore, A, O) T 2 . We conclude this article with a simple application to the isomorphism problem. Theorem 26 (Courcelle [8]) Given two tree interpretable structures A and B of finite tree width one can decide whether A = B. Proof. Although not explicitly stated, the construction of the axiom in the previous section is e#ective. Thus, in order to determine whether A = B one can construct the GSO(# ) formula ....
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On Gödel's Theorems on Lengths of Proofs II: Lower Bounds for.. - Buss (Correct)
....tautologies in a particular special form with known proofs, it can be hard to decide if a shorter proof exists. Thus our proof does not establish any strong new results in complexity theory such as the collapse of the polynomial time hierarchy. An analogous situation occurred in our earlier work [3] where it was shown that the k step provability problem for the first order sequent calculus is undecidable. There we gave a particular integer k and an infinite family of first order formulas, each of which have proofs of k 1 steps, but so that it is undecidable whether a given formula in ....
, The undecidability of k-provability, Annals of Pure and Applied Logic, 53 (1991), pp. 75--102.
On Herbrand's Theorem - Buss (1995) (6 citations) (Correct)
....noting that by removing the E:righl inference from P, a proof of A(x, t) is obtained where A is the quantifier free portion of A . The above theorem can be used to obtain the following no counterexample interpretation which has been very useful recently in the study of bounded arithmetic (see [12,2,18]) 4 Corollary 12. Let T be a universal theory and suppose T (x) Vy)A(x, y, c) with A a quartlifter free formula. There is a k ) 0 and terms t(c) t2(c,y) 4 This corollary is named after the more sophisticated no counterexample interpretations of [13,14] y: v. v y, To prove the ....
--., Relating the bounded arithmetic and polynomial-time hierarchies. To appear, Annals of Pure and Applied Logic, 1997
Axiomatising Tree-Interpretable Structures - Blumensath (2002) (1 citation) (Correct)
....(A, O) is tree interpretable. Proof. O is GSO(# ) definable by the preceding lemma. Since A is of finite treewidth it follows that O is even MSO(# ) definable and, therefore, A, O) We conclude this article with a simple application to the isomorphism problem. Theorem 23 (Courcelle [9]) Given two tree interpretable structures A and B of finite tree width one can decide whether A = B. Proof. Although not explicitly stated, the construction of the axiom in the previous section is e#ective. Thus, in order to determine whether A = B one can construct the GSO(# ) formula ....
, The monadic second-order logic of graphs IV: Definability properties of equational graphs, Annals of Pure and Applied Logic, 49 (1990), pp. 193--255.
Singular Cardinals And The PCF Theory - Jech (1995) (Correct)
....set of cardinals C cofinal in , and destroy all cardinals below that are not in the set C . The technique employed to change the cofinality evolved from Prikry s method, progressing through [42] to [48] More recently, a new method for building models for the negation of SCH was developed in [20] and [22] In Magidor s model [40] 2 # could be as large as # 1 , which was improved by Shelah [54] as to have 2 # = # 1 for any 1 . Woodin [14] constructed a model in which 2 = for all infinite cardinals , and Cummings [9] found a model in which GCH fails exactly at all ....
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The provability logic of \Sigma 1 -interpolability, Annals of Pure and Applied Logic, 64, pp. 1--25. G. K. Japaridze (Dzhaparidze)
Bounded Arithmetic, Cryptography and Complexity - Buss Self-citation (Bounded) (Correct)
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, Relating the bounded arithmetic and polynomial-time hierarchies, Annals of Pure and Applied Logic, 75 (1995), pp. 67--77.
Bounded Arithmetic and Propositional Proof Complexity - Buss (1995) (1 citation) Self-citation (Bounded) (Correct)
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, Relating the bounded arithmetic and polynomial-time hierarchies, Annals of Pure and Applied Logic, 75 (1995), pp. 67--77.
Group Actions On Amorphous Sets - Peter Cameron And Self-citation (Sets) (Correct)
....The presence of Dedekind nite cardinals means that the Axiom of Choice (AC) cannot hold. A set is strictly amorphous if in addition to being amorphous, it is also the case that in any partition of the set into in nitely many pieces, all except nitely many are singletons. Truss and co workers [3, 4, 6] have carried out an extensive study aimed at classi cation of amorphous sets and their neighbours by examining the structure that an amorphous set can carry. This work corroborated the idea that strictly amorphous gives the smallest notion of in nite set. Truss used nite permutation groups ....
....U are in members of of size n( and any left over are in singletons of ; the union of the left over members of has cardinality less than the gauge of . A member of a nitary partition 2 U is called atypical if j j 6= n( The following two properties of an amorphous set are proved in [6]: a) If U is amorphous then (U) is a lattice, and equivalence is a congruence on the lattice. b) For any 2 (U ) there exists 1 2 (U) in standard form equivalent to . Moreover if 2 is also in standard form, and has the same gauge as 1 , then 1 and 2 have an equal number of ....
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J. K. Truss, The structure of amorphous sets, Annals of Pure and Applied Logic, vol. 73 (1995), no. 2, pp. 191-233.
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M. C. Fitting. The logic of proofs, semantically. Annals of Pure and Applied Logic, v. 132, pp. 1--25, 2005.
Chapter Vii - The Logic Of (1968) (1 citation) (Correct)
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The logic of arithmetical hierarchy, Annals of Pure and AppliedLogic, 66, pp. 89--112.
Chapter Vii - The Logic Of (1968) (1 citation) (Correct)
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Bass, S.R., \The undecidability of k-provability", Annals of Pure and Applied Logic, Vol 53, pp 75-102, 1991.
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E. Nelson, The Syntax of Nonstandard Analysis, Annals of Pure and Applied Logic 38, page 123-134, 1988.
Bounded Arithmetic, Proof Complexity and Two Papers of Parikh - Buss (2002) (Correct)
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, The undecidability of k-provability, Annals of Pure and Applied Logic, 53 (1991), pp. 75--102.
On Herbrand's Theorem - Samuel Buss University (1995) (6 citations) (Correct)
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, Relating the bounded arithmetic and polynomial-time hierarchies.To appear, Annals of Pure and AppliedLogic, 199?
Some Remarks on Lengths of Propositional Proofs - Buss (2002) (3 citations) (Correct)
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, The undecidability of k-provability, Annals of Pure and Applied Logic, 53 (1991), pp. 75--102.
Extending ILM with an operator for Σ_1-ness - Goris (2003) (Correct)
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K.N. Ignatiev. The provability logic for # 1 -interpolability. Annals of Pure and Applied Logic, 64:1--25, 1993.
First-Order Proof Theory of Arithmetic - Buss (1998) (5 citations) (Correct)
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Relating the bounded arithmetic and polynomial-time hierarchies, Annals of Pure and Applied Logic, 75, pp. 67--77.
Lovely Pairs of Models - Itay Ben-Yaacov University (Correct)
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E. Casanovas, The number of types in simple theories, Annals of Pure and Applied Logic, 98 (1999), 69-86.
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