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Logic over Words on Denumerable Ordinals

2001
*
Journal of computer and system sciences (Print)
*

and e=; b < d |u b |. 396 NICOLAS BEDON w 2 ABBREV(A, e 1 , s, e 2 )

doi:10.1006/jcss.2001.1782
fatcat:xntww2zetjahtobwvgofm4zwey
*LOGIC**OVER**WORDS**ON**DENUMERABLE**ORDINALS*... If (u b ) b < a is a sequence of*words**over*A then < b < a u b is the*word*v of length ; b < a |u b | defined by, for any c < |v|, where d is the greatest possible*ordinal*such that ; b < d |u b | [ c ...*LOGIC**OVER**WORDS**ON**DENUMERABLE**ORDINALS*Definition 1.5. ...##
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Intuitionism and formalism

1999
*
Bulletin of the American Mathematical Society
*

Let us now consider the concept: "

doi:10.1090/s0273-0979-99-00802-2
fatcat:k3dzfwzjlffavcr3qgs4dmb4ky
*denumerably*infinite*ordinal*number." ...*On*the*one*hand yes, for the number of sentences of at most twenty*words*is of course finite;*on*the other hand no, for if it should exist, it would be defined by the sentence of fifteen*words*formed by ...##
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Intuitionism and formalism

1913
*
Bulletin of the American Mathematical Society
*

Let us now consider the concept: "

doi:10.1090/s0002-9904-1913-02440-6
fatcat:qcjoglfibbclhc26w63544vxta
*denumerably*infinite*ordinal*number." ...*On*the*one*hand yes, for the number of sentences of at most twenty*words*is of course finite;*on*the other hand no, for if it should exist, it would be defined by the sentence of fifteen*words*formed by ...##
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Some consequences of interpreting the associated logic of the first-order Peano Arithmetic PA finitarily
[article]

2012
*
arXiv
*
pre-print

We show that the classical interpretations of Tarski's inductive definitions actually allow us to define the satisfaction and truth of the quantified formulas of the first-order Peano Arithmetic PA

arXiv:1108.4598v2
fatcat:7rq3jrl5wvhjjeykg7n7nhqg6q
*over*... We define this interpretation, and show that if the associated*logic*is interpreted finitarily then (i) PA is categorical and (ii) Goedel's Theorem VI holds vacuously in PA since PA is consistent but not ... implicitly limits its applicability amongst first-order theories to those that are consistent with an axiom of infinity-in the sense that the proof implicitly requires that a constant, say c, along with a*denumerable*...##
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Page 39 of Mathematical Reviews Vol. , Issue 2003A
[page]

2003
*
Mathematical Reviews
*

Belegradek (Istanbul)
See also 12008, 16010, 68053, 68092.
03D Computability and recursion theory
2003a:03058 03D05 03B70 68Q45 68Q70
Bedon, Nicolas (F-MARN-GM; Champs-sur-Marne)

*Logic**over**words**on**denumerable*...*ordinals*. ...##
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Skolem's Paradox and Platonism

1970
*
Crítica. Revista Hispanoamericana de Filosofía
*

. " range

doi:10.22201/iifs.18704905e.1970.88
fatcat:v24vcvnt75dejhzawdtjn63fuu
*over*sets and whose only non-*logical*predicate symbol E stands for the membership relation. ... Skolem, "Some remarks*on*axiomatized set theory", in From Frege to Gödel (a source book in mathematical*logic*, 1879-1931), ed. J. ...##
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Page 1766 of Mathematical Reviews Vol. 54, Issue 6
[page]

1977
*
Mathematical Reviews
*

functions

*on**words*[numbers] as the basic set of relations of a relational structure. ... By a pr-function*over*a set S of*ordinal*numbers we mean a pr-function in whose definition occurs only*ordinal*numbers in S. ...##
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Sets, Set Sizes, and Infinity in Badiou's Being and Event

2020
*
Filozofski Vestnik
*

The necessary structure for Badiou's mathematical ontology in this work was only the

doi:10.3986/fv.41.2.07
fatcat:fi6yf4w7lnfb7modvzmdspbxem
*ordinality*of sets. ... of the*one*, a pluralism of counting that further complicates the relationship between the*one*and the multiple in the post-Cantorian era. ... The*one*qua the result of the count identifies the "other" (the non-*one*) within the "*one*", in other*words*, the immanence of the inconsistent within the consistent. ...##
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Page 1382 of Mathematical Reviews Vol. , Issue 82d
[page]

1982
*
Mathematical Reviews
*

Let T°=I(@); re*'=T(T%(@)); and F8={ Ul*:a<B} if B is a limit

*ordinal*. The closure of I is the union of I'**over*all*ordinals*a. ... If X is the set of*words**on*a finite alphabet, then X is said to be generable if X is the closure of some computable inductive operator. The main result of this paper is the construction of an r.e. ...##
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A non-enumerable well-ordered set

1914
*
Bulletin of the American Mathematical Society
*

In other

doi:10.1090/s0002-9904-1914-02509-1
fatcat:unf4jul5tzhdphxbn4o7b5cxyi
*words*, it is legitimate to postulate two rules of combination-let us call them " lower " and " higher "-whereof the higher is to be distributive*over*the lower, a modulus for the higher rule, ... The present note, based*on*a paper which the writer presented to the Cambridge Congress under the title "Axioms of*ordinal*magnitudes,"* undertakes to show that this question must be answered in the negative ...##
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Contemporary Chemistry: a Survey of the Present State, Methods and Tendencies of Chemical Science

1912
*
Nature
*

*On*p. 81 the symbol » is unfortunately used for the cardinal number of all

*denumerable*sets. ... Among the subjects treated are the meaning of | the elementary | i ass 2 ansfinite

*ordinal*and | . ; properties of classes, and of transfinite

*ordinal*|: = ieeek meee ee, definitions, axioms, and postulates ...

##
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Page 11 of Mathematical Reviews Vol. 51, Issue 1
[page]

1976
*
Mathematical Reviews
*

Let X be a finite alphabet and let y be a directed graph whose nodes are

*words**over*X. ... This is used to interpret P in a ramified second order system with*ordinal*number terms and to define a*denumerable**ordinal*= such that 9, is a model for second order arithmetic, a result first obtained ...##
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Page 1046 of Mathematical Reviews Vol. 20, Issue 10
[page]

1959
*
Mathematical Reviews
*

*On*the theory of

*ordinal*numbers. II. J. Math. Soc. Japan 10 (1958), 106—120. ... If S is a

*logical*system based

*on*the first order predicate calculus, then a choice of a set A of certain well-formed formulas to be axioms yields an elementary theory S(A). ...

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The fundamentals of relations language mathematics
[article]

2012
*
arXiv
*
pre-print

The fundamentals of formal

arXiv:1210.5854v1
fatcat:igqdlxsb2jbvbg7472xgev3bau
*logic*, theory of sets and mathematical structures are narrated in terms of relations language. ... But even for*denumerable*product it is impossible to prove by the above procedure the existence of*one*-to-*one*mapping E N in subset E , since we will not be able to record "*word*", matching any point E ... In regard to potencies scale, its "existence" is easy to be grounded*on*the examples of existence of*denumerable*, non-*denumerable*and non-equivalent sets, for instance Cantor theorem 3.23. ...##
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Brouwer's contributions to the foundations of mathematics

1924
*
Bulletin of the American Mathematical Society
*

"by means of an element invariant

doi:10.1090/s0002-9904-1924-03844-0
fatcat:fwm6xo5oszd6zjnp5opvkssiom
*over*a*denumerably*infinite sequence") enables us to put the proposition as*one*which can be dealt with and decided,*one*way or the other, by the use of complete induction ... -Feb., have used, besides the material referred to above, his book*on*the foundations of mathematics, {*Over*de Grondslagen der Wiskunde, Amsterdam, Maas & van Suchtelen, 1907) and his article*on*the ...
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