An intensional fixed point theory over first order arithmetic

An intensional fixed point theory over first order arithmetic

The purpose of this article is to present a new theory IPA(σ) for fixed points over arithmetic which allows the building up of fixed points in a very nested and entangled way. But in spite of its great expressive power we can show that the proof-theoretic strength of our theory – which is intensional in a meaning to be described below – is characterized by the Feferman-Schütte ordinal Γ0. Our a...

First-order intensional logic

First-order modal logic is very much under current development, with many different semantics proposed. The use of rigid objects goes back to Saul Kripke. More recently several semantics based on counterparts have been examined, in a development that goes back to David Lewis. There is yet another line of research, using intensional objects, that traces back to Richard Montague. I have been invo...

First-Order Proof Theory of Arithmetic

First Order Logic, Fixed Point Logic and Linear Order

The Ordered conjecture of Kolaitis and Vardi asks whether xed point logic di ers from rst order logic on every in nite class of nite ordered structures In this paper we develop the tool of bounded variable element types and illustrate its application to this and the orig inal conjectures of McColm which arose from the study of inductive de nability and in nitary logic on pro cient classes of ni...

Fixed-Point Arithmetic Line Clipping

This algorithm supports line clipping against a rectangular window with edges parallel to the screen. The algorithm combines different partial solutions given in the bibliography such as implicit area codes, decision trees, line ends comparison, symmetry or avoiding redundant calculations, mixing them with fixed-point arithmetic, explicit calculation reusing and dynamic monitoring. It may work ...