scholarly journals Polynomial time operations in explicit mathematics

1997 ◽  
Vol 62 (2) ◽  
pp. 575-594 ◽  
Author(s):  
Thomas Strahm
Keyword(s):  
Polynomial Time ◽  
Proof Theory ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Computable Functions

AbstractIn this paper we study (self-)applicative theories of operations and binary words in the context of polynomial time computability. We propose a first order theory PTO which allows full self-application and whose provably total functions on = {0, 1}* are exactly the polynomial time computable functions. Our treatment of PTO is proof-theoretic and very much in the spirit of reductive proof theory.

A feasible theory for analysis

1994 ◽  
Vol 59 (3) ◽  
pp. 1001-1011 ◽  
Author(s):  
Fernando Ferreira
Keyword(s):  
Polynomial Time ◽  
Order Theory ◽  
Second Order ◽  
First Order ◽  
Weak König’S Lemma ◽  
König’S Lemma ◽  
Computable Functions

AbstractWe construct a weak second-order theory of arithmetic which includes Weak König's Lemma (WKL) for trees defined by bounded formulae. The provably total functions (with -graphs) of this theory are the polynomial time computable functions. It is shown that the first-order strength of this version of WKL is exactly that of the scheme of collection for bounded formulae.

scholarly journals GEOMETRISATION OF FIRST-ORDER LOGIC

2015 ◽  
Vol 21 (2) ◽  
pp. 123-163 ◽  
Author(s):  
ROY DYCKHOFF ◽  
SARA NEGRI
Keyword(s):  
Proof Theory ◽  
Normal Forms ◽  
Order Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Conservative Extension ◽  
First Order ◽  
First Order Theory ◽  
Intermediate Logics ◽  
Normal Form Theorem

AbstractThat every first-order theory has a coherent conservative extension is regarded by some as obvious, even trivial, and by others as not at all obvious, but instead remarkable and valuable; the result is in any case neither sufficiently well-known nor easily found in the literature. Various approaches to the result are presented and discussed in detail, including one inspired by a problem in the proof theory of intermediate logics that led us to the proof of the present paper. It can be seen as a modification of Skolem’s argument from 1920 for his “Normal Form” theorem. “Geometric” being the infinitary version of “coherent”, it is further shown that every infinitary first-order theory, suitably restricted, has a geometric conservative extension, hence the title. The results are applied to simplify methods used in reasoning in and about modal and intermediate logics. We include also a new algorithm to generate special coherent implications from an axiom, designed to preserve the structure of formulae with relatively little use of normal forms.

scholarly journals A first-order theory of Ulm type

Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 347-358
Author(s):  
Matthew Harrison-Trainor
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory

scholarly journals Quasi-decidability of a Fragment of the First-Order Theory of Real Numbers

2015 ◽  
Vol 57 (2) ◽  
pp. 157-185 ◽  
Author(s):  
Peter Franek ◽  
Stefan Ratschan ◽  
Piotr Zgliczynski
Keyword(s):  
Order Theory ◽  
Real Numbers ◽  
First Order ◽  
First Order Theory

The spectrum of resplendency

1990 ◽  
Vol 55 (2) ◽  
pp. 626-636
Author(s):  
John T. Baldwin
Keyword(s):  
Homogeneous Model ◽  
Order Theory ◽  
First Order ◽  
First Order Theory ◽  
Uncountable Cardinal ◽  
Recursive Theory ◽  
Finite Language

AbstractLet T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least min(2λ, ℶ2) resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, 2ω} there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ.

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