A decidable variety that is finitely undecidable

1999 ◽  
Vol 64 (2) ◽  
pp. 651-677
Author(s):  
Joohee Jeong
Keyword(s):  
Finite Type ◽  
Order Theory ◽  
First Order ◽  
Finite Models ◽  
First Order Theory

AbstractWe construct a decidable first-order theory T such that the theory of its finite models is undecidable. Moreover, T will be equationally axiomatizable and of finite type.

Analysis without actual infinity

1981 ◽  
Vol 46 (3) ◽  
pp. 625-633 ◽  
Author(s):  
Jan Mycielski
Keyword(s):  
Natural Science ◽  
Order Theory ◽  
Finite Part ◽  
Consistency Proof ◽  
Actual Infinity ◽  
First Order ◽  
Finite Models ◽  
First Order Theory ◽  
Potential Applications

AbstractWe define a first-order theory FIN which has a recursive axiomatization and has the following two properties. Each finite part of FIN has finite models. FIN is strong enough to develop that part of mathematics which is used or has potential applications in natural science. This work can also be regarded as a consistency proof of this hitherto informal part of mathematics. In FIN one can count every set; this permits one to prove some new probabilistic theorems.

An Example of a Complete First-Order Theory with All Models Algorithmically Trivial but Without Locally Finite Models

1982 ◽  
Vol 5 (3-4) ◽  
pp. 313-318
Author(s):  
Paweł Urzyczyn
Keyword(s):  
Order Theory ◽  
Complete Theory ◽  
Prime Model ◽  
Program Schema ◽  
Locally Finite ◽  
First Order ◽  
Finite Models ◽  
First Order Theory

We show an example of a first-order complete theory T, with no locally finite models and such that every program schema, total over a model of T, is strongly equivalent in that model to a loop-free schema. For this purpose we consider the notion of an algorithmically prime model, what enables us to formulate an analogue to Ryll-Nardzewski Theorem.

scholarly journals THE LINDENBAUM ALGEBRA OF THE THEORY OF THE CLASS OF ALL FINITE MODELS

2002 ◽  
Vol 02 (02) ◽  
pp. 145-225 ◽  
Author(s):  
STEFFEN LEMPP ◽  
MIKHAIL PERETYAT'KIN ◽  
REED SOLOMON
Keyword(s):  
Boolean Algebra ◽  
Order Theory ◽  
Boolean Algebras ◽  
Quotient Algebra ◽  
First Order ◽  
Finite Models ◽  
First Order Theory ◽  
Recursive Isomorphism ◽  
Atomic Boolean Algebra

In this paper, we investigate the Lindenbaum algebra ℒ(T fin ) of the theory T fin = Th (M fin ) of the class M fin of all finite models of a finite rich signature. We prove that this algebra is an atomic Boolean algebra while its Gödel numeration γ is a [Formula: see text]-numeration. Moreover, the quotient algebra (ℒ(T fin )/ℱ, γ/ℱ) modulo the Fréchet ideal ℱ is a [Formula: see text]-algebra, which is universal over the class of all [Formula: see text] Boolean algebras. These conditions characterize uniquely the algebra ℒ(T fin ); moreover, these conditions characterize up to recursive isomorphism the numerated Boolean quotient algebra (ℒ(T fin )/ℱ, γ/ℱ). These results extend the work of Trakhtenbrot [17] and Vaught [18] on the first order theory of the class of all finite models of a finite rich signature.

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
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