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Logic over Words on Denumerable Ordinals

Nicolas Bedon
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 ) 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.  ... 
doi:10.1006/jcss.2001.1782 fatcat:xntww2zetjahtobwvgofm4zwey

Intuitionism and formalism

Dr. L. E. J. Brouwer
1999 Bulletin of the American Mathematical Society  
Let us now consider the concept: "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  ... 
doi:10.1090/s0273-0979-99-00802-2 fatcat:k3dzfwzjlffavcr3qgs4dmb4ky

Intuitionism and formalism

L. E. J. Brouwer
1913 Bulletin of the American Mathematical Society  
Let us now consider the concept: "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  ... 
doi:10.1090/s0002-9904-1913-02440-6 fatcat:qcjoglfibbclhc26w63544vxta

Some consequences of interpreting the associated logic of the first-order Peano Arithmetic PA finitarily [article]

Bhupinder Singh Anand
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 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  ... 
arXiv:1108.4598v2 fatcat:7rq3jrl5wvhjjeykg7n7nhqg6q

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.  ... 

Skolem's Paradox and Platonism

Carlo Cellucci
1970 Crítica. Revista Hispanoamericana de Filosofía  
. " range 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.  ... 
doi:10.22201/iifs.18704905e.1970.88 fatcat:v24vcvnt75dejhzawdtjn63fuu

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.  ... 

Sets, Set Sizes, and Infinity in Badiou's Being and Event

Tzuchien Tho
2020 Filozofski Vestnik  
The necessary structure for Badiou's mathematical ontology in this work was only the 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.  ... 
doi:10.3986/fv.41.2.07 fatcat:fi6yf4w7lnfb7modvzmdspbxem

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.  ... 

A non-enumerable well-ordered set

A. B. Frizell
1914 Bulletin of the American Mathematical Society  
In other 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  ... 
doi:10.1090/s0002-9904-1914-02509-1 fatcat:unf4jul5tzhdphxbn4o7b5cxyi

Contemporary Chemistry: a Survey of the Present State, Methods and Tendencies of Chemical Science

F. G. D.
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  ... 
doi:10.1038/088410a0 fatcat:ldnksgpz3jflvfyf6ryutcz5ge

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  ... 

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).  ... 

The fundamentals of relations language mathematics [article]

V. Ye. Mitroshin
2012 arXiv   pre-print
The fundamentals of formal 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.  ... 
arXiv:1210.5854v1 fatcat:igqdlxsb2jbvbg7472xgev3bau

Brouwer's contributions to the foundations of mathematics

Arnold Dresden
1924 Bulletin of the American Mathematical Society  
"by means of an element invariant 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  ... 
doi:10.1090/s0002-9904-1924-03844-0 fatcat:fwm6xo5oszd6zjnp5opvkssiom
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