Algebraic theory of quasivarieties of heterogeneous partial algebras

Studia Logica ◽  
2004 ◽  
Vol 78 (1-2) ◽  
pp. 129-153
Author(s):  
Peter Burmeister
Keyword(s):  
Algebraic Theory ◽  
Partial Algebras

Algebra of constructions II: an algebraic approach to Martin-Löf type theory and the calculus of constructions

1993 ◽  
Vol 3 (1) ◽  
pp. 63-92
Author(s):  
Adam Obtułowicz
Keyword(s):  
Type Theory ◽  
Algebraic Theory ◽  
Algebraic Approach ◽  
Recursive Functions ◽  
Algebraic Theories ◽  
Calculus Of Constructions ◽  
Partial Algebras

We present an algebraic approach to the syntax and semantics of Martin-Löf type theory and the calculus of constructions developed by T. Coquand and G. Huet. In our approach, models of this theory and this calculus are treated as three-sorted partial algebras, called ITSΠ-structures, described by essentially algebraic theories. We give a proof that derived statements of Martin-Löf type theory hold in appropriate ITSΠ-structures. In this proof, a formal translation from the language of terms and types into the language of terms of an appropriate essentially algebraic theory of ITSΠ-structures is used. A straightforward set-theoretic construction of ITSΠ-structures that are models of Martin-Löf type theory is demonstrated. We present a construction of a recursive ITSΠ-structure(i.e. its partial and total operations are recursive functions over some alphabet) that is a model of the calculus of constructions and demonstrates the decidability of this calculus.

Affine algebraic sets relative to an algebraic theory

1999 ◽  
Vol 65 (1-2) ◽  
pp. 54-76 ◽  
Author(s):  
Yves Diers
Keyword(s):  
Algebraic Theory ◽  
Algebraic Sets

PUSHOUTS OF PARTIAL HOMOMORPHISMS OF PARTIAL ALGEBRAS II: CLOSED QUOMORPHISMS

2003 ◽  
Vol 02 (04) ◽  
pp. 471-500
Author(s):  
R. ALBERICH ◽  
F. ROSSELLÓ
Keyword(s):  
Basic Problem ◽  
Arbitrary Signature ◽  
Partial Algebras

We characterize the pairs of closed homomorphisms and closed quomorphisms of partial Σ-algebras that have a pushout in the corresponding category, for an arbitrary signature Σ. The latter characterization solves the basic problem previous to the development of a single-pushout approach to the transformation of partial algebras based on closed quomorphisms.

The Algebraic Theory of Semigroups, Vol. I

1964 ◽  
Vol 48 (363) ◽  
pp. 122
Author(s):  
W. D. Munn ◽  
A. H. Clifford ◽  
G. B. Preston
Keyword(s):  
Algebraic Theory
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