1922b onward, consisted in what he called the finitary standpoint.    From Wordnik.com.  [Hilbert's Program] Reference

If it also satisfies (4) it is said to be finitary.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

Now suppose there were a finitary consistency proof of T.    From Wordnik.com.  [Hilbert's Program] Reference

Conversely, if a quasivariety is an Eq-algebraic semantics for a finitary.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

If in addition C satisfies (3) we say that it is a finitary consequence operation.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

P, P itself (or the finitary proposition it expresses) must be finitarily provable.    From Wordnik.com.  [Hilbert's Program] Reference

Blok and Pigozzi defined the notion of algebraizable logic only for finitary logics.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

L be a finitary and finitely algebraizable logic with the deduction-detachment property.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

The most basic judgments about finitary numerals are those about equality and inequality.    From Wordnik.com.  [Hilbert's Program] Reference

Using (2) it gives the isomorphism theorem for finitary and finitely algebraizable logics.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

The more interesting conceptual issue is which operations should be considered as finitary.    From Wordnik.com.  [Hilbert's Program] Reference

For example it is known (see (Czelakowski, 2001)) that for every finitary protoalgebraic logic.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

There are several basic and interrelated issues in understanding Hilbert's finitary standpoint.    From Wordnik.com.  [Hilbert's Program] Reference

The result is the same: finitary provability turns out to be coextensive with provability in PA.    From Wordnik.com.  [Hilbert's Program] Reference

Bernays (1930) explained how exponentiation may be understood as a finitary operation on numerals.    From Wordnik.com.  [Hilbert's Program] Reference

Show, using finitary methods, that each proof in the extended system has a consistent interpretation.    From Wordnik.com.  [The Epsilon Calculus] Reference

The domain of contentual number theory consists in the finitary numerals, i.e., sequences of strokes.    From Wordnik.com.  [Hilbert's Program] Reference

It is mysterious why Hilbert wanted to prove directly the consistency of analysis by finitary methods.    From Wordnik.com.  [Kurt Gödel] Reference

The consistency proof itself was to be carried out using only what Hilbert called “finitary” methods.    From Wordnik.com.  [Hilbert's Program] Reference

Thus, checking the validity of a formula of L is equivalent to performing a finite number of finitary tests.    From Wordnik.com.  [Combining Logics] Reference

If such a set exists and the logic is finitary, one can always find a finite subset with the same properties.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

For many other finitary and finitely algebraizable logics to find a convincing explanation is still an open problem.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

All the methods of finitary reasoning used in the consistency proofs up till then were believed to be formalizable in.    From Wordnik.com.  [Hilbert's Program] Reference

Contentual induction was accepted in its application to finitary statements of the hypothetical, general kind explicitly in.    From Wordnik.com.  [Hilbert's Program] Reference

It yields the result that exactly those functions are finitary which can be proved to be total in first-order arithmetic PA.    From Wordnik.com.  [Hilbert's Program] Reference

The special epistemological character of finitary reasoning then yields the required justification of classical mathematics.    From Wordnik.com.  [Hilbert's Program] Reference

Bernays (1930), of which Hilbert's article “On the infinite” provides the most detailed elaboration of the finitary standpoint.    From Wordnik.com.  [Hilbert's Program] Reference

Similarly, finitary judgments may involve not just equality or inequality but also basic decidable properties, such as “is a prime.”.    From Wordnik.com.  [Hilbert's Program] Reference

Another interesting analysis of finitary proof, which, however, does not provide as detailed a philosophical justification, was proposed by.    From Wordnik.com.  [Hilbert's Program] Reference

The correspondence principle and finitary ergodi.    From Wordnik.com.  [Feeds4all documents in category 'SEO'] Reference

A finitary analogue of the Lebesgue decomposition (optional).    From Wordnik.com.  [What's new] Reference

2.2 Finitarily meaningful propositions and finitary reasoning.    From Wordnik.com.  [Hilbert's Program] Reference

PA, are nonetheless finitary.    From Wordnik.com.  [Hilbert's Program] Reference

‰ Š¢ C and if is finitary, so is.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

A finitary and finitely algebraizable logic.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

What are the objects of finitary reasoning?.    From Wordnik.com.  [Hilbert's Program] Reference

This principle includes the finitary version.    From Wordnik.com.  [Wild Dreams Of Reality, 3] Reference

It is finitary if in addition it satisfies if X.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

L is finitary if.    From Wordnik.com.  [Propositional Consequence Relations and Algebraic Logic] Reference

2.3 finitary operations and finitary proof.    From Wordnik.com.  [Hilbert's Program] Reference