Results 1 
2 of
2
A Simple Theory of Expressions, Judgments and Derivations
 ASIAN 2004, Lecture Notes in Computer Science 3321
, 2004
"... Abstract. We propose a simple theory of expressions which is intended to be used as a foundational syntactic structure for the Natural Framework (NF). We define expression formally and give a simple proof of the decidability of αequivalence. We use this new theory of expressions to define judgments ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Abstract. We propose a simple theory of expressions which is intended to be used as a foundational syntactic structure for the Natural Framework (NF). We define expression formally and give a simple proof of the decidability of αequivalence. We use this new theory of expressions to define judgments and derivations formally, and we give concrete examples of derivation games to show a flavor of NF. 1
A New Approach to Predicative Set Theory
"... We suggest a new basic framework for the WeylFeferman predicativist program by constructing a formal predicative set theory PZF which resembles ZF. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an a ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We suggest a new basic framework for the WeylFeferman predicativist program by constructing a formal predicative set theory PZF which resembles ZF. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. This idea is implemented using syntactic safety relations between formulas and sets of variables. These safety relations generalize both the notion of domainindependence from database theory, and Godel notion of absoluteness from set theory. The language of PZF is typefree, and it reflects real mathematical practice in making an extensive use of statically defined abstract set terms. Another important feature of PZF is that its underlying logic is ancestral logic (i.e. the extension of FOL with a transitive closure operation). 1