The decision problem for standard classes

@article{Gurevich1976TheDP,
  title={The decision problem for standard classes},
  author={Yuri Gurevich},
  journal={Journal of Symbolic Logic},
  year={1976},
  volume={41},
  pages={460 - 464}
}
  • Y. Gurevich
  • Published 1 June 1976
  • Mathematics
  • Journal of Symbolic Logic
The standard classes of a first-order theory T are certain classes of prenex T-sentences defined by restrictions on prefix, number of monadic, dyadic, etc. predicate variables, and number of monadic, dyadic, etc. operation variables. In [3] it is shown that, for any theory T, (1) the decision problem for any class of prenex T-sentences specified by such restrictions reduces to that for the standard classes, and (2) there are finitely many standard classes K 1, …, Kn such that any undecidable… 

0-1 LAWS FOR FRAGMENTS OF SECOND-ORDER LOGIC: AN OVERVIEW

The probability of a property on the collection of all finite relational structures is the limit as n --< infinity of the fraction of structures with n elements satisfying the property, provided the

0-1 laws and decision problems for fragments of second-order logic

Complexity Results for First-Order Two-Variable Logic with Counting

TLDR
It is proved that the satisfiability problem for first-order sentences with two variables and with additional quantifiers "there exists exactly (at most, at least) $i$" for $i\leq p$ is NEXPTIME-complete.

Undecidability results on two-variable logics

TLDR
It is shown that going beyond L2 by adding any one of the following leads to an undecidable logic: very weak forms of recursion, such as transitive closure or monadic fixed-point operations.

Size of Models versus Length of Computations: On Inseparability by Nondeterministic Time Complexity Classes

TLDR
It is proved that his can be reached for most undecidable prefix vocabulary classes and for some formula classes the size of the models is larger than the length of the computations that they can describe, so the inseparability results are weaker.

First-Order Queries over One Unary Function

TLDR
This paper proves a form of quantifier elimination result: any query defined by a quasi-unary first-order formula can be equivalently defined, up to a suitable linear-time reduction, by a quantifier-free formula, and reproves that such queries can be computed in total time.

Goldfarb 1984 ) ( Kahr 1962 ) ( Goldfarb 1984 ) ( Kahnar , Suranyi 1950 ) ( Denton 1963 ) ( Suranyi

A b s t r a c t . Starting from the classification of prefix vocabulary classes in first order logic (with functions) with respect to decidability/undecidability and from Trakhtenbrots Inseparability

Decidability of cylindric set algebras of dimension two and first-order logic with two variables

TLDR
A new proof for the decidability and finite model property of first-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig, is given, which shows the known results that the universal theory of Pse, is decidable and that every finite Pse2 can be represented on a finite base.
...

References

SHOWING 1-10 OF 12 REFERENCES

Decidability of second-order theories and automata on infinite trees

Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involves

Remarks on Berger's paper on the domino problem

The domino concept was introduced by Hao Wang [2] and is related to the decision problem for the formulas of the predicate calculus with the pref ixAEA (i.e., an existential quantifier between two

Some Reduction Classes and Undecidable Theories

We call a formula of E Д type an arbitrary formula of predicate calculus with equality and functional symbols which has the form $$\exists \,x\,D,$$ where x is the subject variable, D is the

Zum Entscheidungsproblem des logischen Funktionenkalküls

The decision problem for the logic of predicates and of operations

Most work on the decision problem for the logic of predicates belongs to the class of preliminary formulas, posed in a way limited to prefixes and predicate variables. These investigations have

On the effective recognizing of satisfiability of predicate formulas

  • Algebra and Logic, vol. 5
  • 1966

The reduction class VxVy3zF(x

  • y, z) A VnA(F), Cybernetics (Kiev, USSR)
  • 1971

On the effective recognizing of satisfiability of predicate formulas, Algebra and Logic

  • On the effective recognizing of satisfiability of predicate formulas, Algebra and Logic
  • 1966

The reduction class VxVy3zF(x,y,z) A VM(F)

  • Cybernetics (Kiev, USSR),
  • 1971