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Projects / Programmes source: ARRS

Popolnost linearne logike z vidika omejenih strukturnih pravil (Slovene)

Research activity

Code Science Field Subfield
1.01.04  Natural sciences and mathematics  Mathematics  Algebra 

Code Science Field
P110  Natural sciences and mathematics  Mathematical logic, set theory, combinatories 
Keywords
Free ordered algebra, free lattice, complete class of models, game semantics, partion theorem, forcing.
Evaluation (rules)
source: COBISS
Researchers (2)
no. Code Name and surname Research area Role Period No. of publications
1.  20757  PhD Gregor Dolinar  Mathematics  Researcher  2000 - 2002  13 
2.  05954  PhD Andreja Prijatelj  Mathematics  Principal Researcher  2000 - 2002  56 
Organisations (1)
no. Code Research organisation City Registration number No. of publications
1.  0101  Institute of Mathematics, Physics and Mechanics  Ljubljana  5055598000  19,308 
Abstract
This project proposal may essentially be seen as a continuation of the research work on linear logic in view of bounded structural rules with its main stream directed towards: (i) further development of the corresponding free ordered algebraic structures, in particular, a generation of a free lattice over free partially ordered algebras; (ii) constructions of complete classes of models for specific axiomatic systems of linear logic without the modalities that can be embedded into linear logic faithfully. Ultimately, a solution of this problem should yield a natural complete semantics, other than purely algebraic, for full propositional linear logic (an open problem from 1987). And finally, a useful link of proving techniques in logic with those in set theory will be given by examining: (iii) a relation between two versions of a proof of the independence of the axiom of choice in Zermelo-Fraenkel set theory. The first one based on the partition theorem in the sense of Ramsey and the second one on the famous Cohen method of forcing.
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