• Corpus ID: 55522614

# Arithmetical extensions of relational systems

```@article{Tarski1958ArithmeticalEO,
title={Arithmetical extensions of relational systems},
author={Alfred Tarski and Robert L. Vaught},
journal={Compositio Mathematica},
year={1958},
volume={13},
pages={81-102}
}```
• Published 1958
• Mathematics
• Compositio Mathematica
© Foundation Compositio Mathematica, 1956-1958, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
241 Citations
Degrees of Unsolvability of Constructible Sets of Integers
• Computer Science, Mathematics
J. Symb. Log.
• 1968
Why the Post-Kleene arithmetical hierarchy of degrees of (recursive) unsolvability was extended into the transfinite is not clear, but there is some evidence that it was once hoped that a theorem for the analytical hierarchy analogous to the result of Post and Kleene would be found.
Sur La Theorie Elementaire Des Corps De Fonctions
On etudie la theorie du premier ordre des corps de fonctions dans le langage des corps en utilisant les resultats fondamentaux sur les courbes en geometrie algebrique. On donne quelques applications
Non-Standard Models of Arithmetic: a Philosophical and Historical perspective
• Mathematics
• 2010
Over the last fifty years, the study of non-standard models of arithmetic has become a fertile and highly technical mathematical branch. Nevertheless, surprising as it might seem today, the topic of
Algumas aplicações algébricas da teoria dos modelos
Let K be an algebraically closed field. We say that a subset of K, where n is a positive natural number, is constructible if it is a boolean combination of Zariski closed sets. In Model Theory, a
Modelle der Arithmetik
• Philosophy
• 1990
Sei A ein Axiomensystem erster Stufe fur die Theorie der ganzen (positiven und negativen) Zahlen; A enthalte 0, 1, Addition und Multiplikation und eventuell abzahlbar unendlich viele weitere
Tarski's Influence on Computer Science
Alfred Tarski played one of the leading roles in the development of mathematical logic in the twentieth century, as much for the programs he promoted and the conceptual organization of the subject as for his many important results.
Tarski's influence on computer science
• S. Feferman
• Computer Science, Mathematics
20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
• 2005
Alfred Tarski played one of the leading roles in the development of mathematical logic in the twentieth century, as much for the programs he promoted and the conceptual organization of the subject as for his many important results.
Properties preserved under algebraic constructions
The study of properties of algebras belongs equally to Algebra and to Metamathematics. But here we consider only questions that concern all abstract algebras, and we attempt to discuss them without
Bases for First-Order Theories and Subtheories
• W. Craig
• Mathematics, Computer Science
J. Symb. Log.
• 1960
What degree of economy, or at least regularity, can be achieved for all recursively axiomatizable first-order theories is investigated.

## References

SHOWING 1-10 OF 15 REFERENCES
Some interconnections between modern algebra and mathematical logic
Mathematical logic originated when mathematical methods were brought to bear on traditional questions of logic, especially the problem of what constitutes a valid proof. For the most part work in
On the Axiom of Choice and some metamathematical theorems
• Bulletin of the American Mathematical Society
• 1956
On the arithmetical equivalence of free algebras
• Bulletin of the American Mathematical Society
• 1955
Product operations on relational systems
• Bulletin of the American Mathematical Society
• 1955
Sum operations on relational systems
• Bulletin of the American Mathematical Society
• 1955
Contributions to the theory of models. Parts I and II
• part III, ibidem
• 1954
Topics in the theory of arithmetical classes and boolean algebras. Doctoral dissertation
• 1954
Logisch-kombinatorisch Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen
• Products of abstract algebras. Fundamenta Mathematicae,
• 1952
On Direct Products of Theories