A. Tarski. Sur les ensembles fini. Fundamenta Mathematicae, 6:45--95, 1924. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
An Equational Re-Engineering of Set Theories - Formisano, Omodeo (1998) (Correct)
....this approach from its restrained version Total( r( 0 ffi3 1 ffiP ) Under the set axioms (E) Pow) S) Pair) introduced so far, it is reasonable to characterize a set a as being finite if and only if every set b of which a is an element has an element which is minimal w.r.t. inclusion (cf. [20], p.49) Intuitively speaking, in fact, the set formed by all infinite cs in the power set ( a ) of a has no minimal elements when a is This was one of the first major theorems whose proof was automatically found by a theorem prover, cf. 1] This achievement originally took place in the ....
A. Tarski. Sur les ensembles fini. Fundamenta Mathematicae, 6:45--95, 1924.
Solvable set/hyperset contexts: I. Some decision procedures.. - Omodeo, Policriti (Correct)
....9 t ( Y 2 t 8 u 2 t 8 v 2 u v 2 t ) Powerset. 9 p 8 v( 8 z 2 v v 2 Y ) v 2 p) Finiteness. F 2 K 9 a 2 K 8 b 2 K ( b 6= a 9 d 2 b d = 2 a ) finally (A) if present, ought to be replaced by regularity (see preamble of Lemma 5) The above formulation of finiteness originates from [Tar24]. 2 4 Flexes and their decorations To set the ground for the proof methods of Sections 6 and 7, we need to generalize our discourse to structures somewhat richer than graphs, creating a link between this paper and [OPP95, OPP93] Definition 9. A flex is a directed graph G whose nodes are ....
A. Tarski. Sur les ensembles fini. Fundamenta Mathematicae, VI:45--95, 1924.
Some Aspects and Examples of Infinity Notions - Degen (1994) (Correct)
....T extending ZF . Around this definition we organize some old and new notions of infinity; we also indicate some easy independence proofs. 1 Introduction The investigation of different definitions of infinity constitutes a significant part of the development of axiomatic set theory. Tarski [15], Mostowski [11] L evy [9] and many other authors have devoted research papers to the theme of finiteness definitions (which is the most often used term for this subject) The finiteness definitions one usually comes across are all mutually equivalent if the full Axiom of Choice (AC) is adopted ....
....no permutation g of x such that f ffi g ffi f = f where ffi denotes functional composition. 4) The set x is strongly Tarski infinite iff there is a chain (y i ) i2 in the powerset of x without a maximal element. Note: this is only one of the notions of infinity considered by Tarski, see [15]) 5) The set x is almost Dedekind infinite iff p(x) is Dedekind infinite. 6) The set x is star infinite iff there is an f : p (x) p (x) where p (x) is the set of finite subsets of x) such that for all y 2 p (x) f(y) 6 y. 7) The set x is strongly star infinite iff there is an f : ....
A. Tarski "Sur les ensembles finis"Fund. Math. vol. 6 (1924) 45-95
An Equational Re-Engineering of Set Theories - Formisano, Omodeo (1998) (Correct)
....approach from its restrained version Total( r( 0 ffi3 1 ffiP ) Under the set axioms (E) Pow) S) Pair) introduced so far, it is reasonable to characterize a set a as being finite if and only if every set b of which a is an element has an element which is minimal w.r.t. inclusion (cf. [20], p.49) Intuitively speaking, in fact, the set formed by all infinite cs in the power set ( a ) of a has no minimal elements when a is 2 This was one of the first major theorems whose proof was automatically found by a theorem prover, cf. 1] This achievement originally took place in the ....
A. Tarski. Sur les ensembles fini. Fundamenta Mathematicae, 6:45--95, 1924.
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