The proof-theoretic analysis of transfinitely iterated quasi least fixed points

The proof-theoretic analysis of transfinitely iterated quasi least fixed points

The starting point of this article is an old question asked by Feferman in his paper on Hancock’s conjecture [6] about the strength of ID1. This theory is obtained from the well-known theory ID1 by restricting fixed point induction to formulas that contain fixed point constants only positively. The techniques used to perform the proof-theoretic analysis of ID1 also permit to analyze its transfi...

Proof-theoretic analysis by iterated reflection

Progressions of iterated reflection principles can be used as a tool for ordinal analysis of formal systems. Technically, in some sense, they replace the use of omega-rule. We compare the information obtained by this kind of analysis with the results obtained by the more usual proof-theoretic techniques. In some cases the techniques of iterated reflection principles allows to obtain sharper res...

Proof-theoretic aspects of modal logic with fixed points

Quasi Contraction and Fixed Points

In this note, we establish and improve some results on fixed point theory in topological vector spaces. As a generalization of contraction maps, the concept of quasi contraction multivalued maps on a topological vector space will be defined. Further, it is shown that a quasi contraction and closed multivalued map on a topological vector space has a unique fixed point if it is bounded value.

On the fixed points of the iterated pseudopalindromic closure operator

First introduced in the study of the Sturmian words, the iterated palindromic closure was generalized to pseudopalindromes. This operator allows one to construct words with infinitely many pseudopalindromic prefixes, called pseudostandard words. We provide here several combinatorial properties of the fixed points under the iterated pseudopalindromic closure.