Hans Lauchli, "A decision procedure for the weak second-order theory of linear order", In "Contributions to Mathematical Logic", eds. H. A. S hmidt et al., North Holland, 1968, 189--197.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... origins of the composition method can be traced back to the FefermanVaught article on the first order properties of products of algebraic systems [4] Lauchli introduced d theories in the context of weak monadic secondorder logic; he proved that the weak MSO theory of linear order is decidable [11]. The weak MSO is the version of MSO where second order quantification is restricted to finite sets. Shelah generalized the method to full MSO and used it in particular to prove in a uniform way all known decidability results for the MSO theories of various classes of linear orders [15] He ....

Hans Lauchli, "A decision procedure for the weak second-order theory of linear order", In "Contributions to Mathematical Logic", eds. H. A. Schmidt et al., North Holland, 1968, 189--197.

....presented in [Barwise, 1973] This theorem is as follows: Theorem 2.10 ( Scott, 1965] For every countable structure A , there is a sentence, OE 2 L 1 , such that for any countable structure B , B j= OE if and only if A = B . A similar construction to the one given below also appeared in [Lauchli, 1968] and was used in [Shelah, 1975] and [Gurevich, 1979] For the purpose of this section, we will assume that there are no constants in the language being considered. The results can be easily generalized to the case where constants are present. Let A be a structure, A the universe of A and let S = ....

H. Lauchli. A decision procedure for the weak second order theory of linear order. In H.A. Schmidt, K. Schutte, and H.-J. Thiele, editors, Contributions to Mathematical Logic, pages 189--197. North Holland, 1968.

....an equivalent Kn formula # # # # 2 # # 2 by Cor. 3.3.6, and further an equivalent ordinary Buchi automaton A by Theorem 3.4.18. Deciding the emptiness of the automaton A is then easy. Originally the decidability result for WSnS was first established by Doner [23] and for WS1S by Lauchli [57]. This correspondence of Theorem 3.4.18 between Buchi automata and the alternation class # 2 was first reported by Arnold and Niwinski in [3] with a proof outline using a di#erent technique from the one here. For a weaker language, essentially without conjunction, the result was shown earlier by ....

Lauchli, H.: A decision procedure for the weak second-order theory of linear order, in Schutte, K. (ed.): Contributions to Mathematical Logic,North- Holland, 1968, pp. 189-197

....in the proof of Proposition 33 for the case of prime spiders. 2 4.3 The Feferman Vaught Theorem In the proof of Theorem 4 we shall use a version of the Feferman Vaught Theorem, FV59] adapted to MSOL. It is not clear who observed first that this adaptation to MSOL is true, but it is already in [Lau68, She75] and follows from [Fef57, Ehr61] For a good exposition, cf. Gur79, Gur85] We review some notation from [CM93] Definition34. Let A be a structure, let A be the domain of A and let be a MSOL( formula with free set variables X 1 ; Xn . We denote by sat(A; the set of n tuples of ....

H. Lauchli. A decision procedure for the weak second order theory of linear order. In Logic Colloquium '66, pages 189--197. North Holland, 1968.

....theorem [Scott, 1965] as presented in [Barwise, 1973] This theorem is as follows: Theorem 6 ( Scott, 1965] For every countable structure A , there is a sentence, OE 2 L 1 , such that for any countable structure B , B j= OE if and only if A = B . A similar construction also appeared in [Lauchli, 1968] and was used in [Shelah, 1975] and [Gurevich, 1979] For the purpose of this section, we will assume that there are no constants in the language being considered. The results can be easily generalized to the case where constants are present. Let A be the universe of A and let S = A k be the ....

H. Lauchli. A decision procedure for the weak second order theory of linear order. In H.A. Schmidt, K. Schutte, and H.-J. Thiele, editors, Contributions to Mathematical Logic, pages 189--197. North Holland, 1968.

....in C. This might be useful in an attempt to solve problem 16. 3.3 The Feferman Vaught Theorem In the proof of Theorem 4 we shall use a version of the Feferman Vaught Theorem, FV59] adapted to MSOL. It is not clear who observed first that this adaptation to MSOL is true, but it is already in [Lau68, She75] and follows from [Fef, Ehr61] For a good exposition, cf. Gur79, Gur85] We review some notation from [CM93] Definition22. Let A be a structure, let A be the domain of A and let be a MSOL( formula with free set variables X 1 ; Xn . We denote by sat(A; the set of subsets of A ....

H. Lauchli. A decision procedure for the weak second order theory of linear order. In Logic Colloquium '66, pages 189--197. North Holland, 1968.

No context found.

Hans Lauchli, "A decision procedure for the weak second-order theory of linear order", In "Contributions to Mathematical Logic", eds. H. A. S hmidt et al., North Holland, 1968, 189--197.

No context found.

H. Lauchli. A decision procedure for the weak second order theory of linear order. In Contributions to Mathematical Logic, Proceedings of Logic Colloquium Hanover 1966.

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