Hyperarithmetical quantifiers

Hyperarithmetical Sets

1. Preamble: Kleene [1943], Post [1944] and Mostowski [1947] . . . . . . . . . 2 1A. Post’s degrees of unsolvability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1B. Kleene’s arithmetical hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1C. Kleene [1943] vs. Post [1944] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1D. Mostowski [1...

Intrinsically Hyperarithmetical Sets

The main result proved in the paper is that on every recursive structure the intrinsically hyperarithmetical sets coincide with the relatively intrinsically hyperarithmetical sets. As a side eeect of the proof an eeective version of the Kueker's theorem on deenability by means of innnitary formulas is obtained. 1. Introduction One of the main achievements of the classical recursion theory is th...

Hyperarithmetical Index Sets in Recursion Theory

We define a family of properties on hyperhypersimple sets and show that they yield index sets at each level of the hyperarithmetical hierarchy. An extension yields a nj-complete index set. We also classify the index set of quasimaximal sets, of coinfinite r.e. sets not having an atomless superset, and of r.e. sets major in a fixed nonrecursive r.e. set. 0. Introduction. The present paper deals ...

Quantifiers ∗

Quantifiers are terms of generality. They are also among our prime examples of operators which take scope. The distinction between singular and general terms, as well as the ways that general terms enter into scope relations, are certainly fundamental to our understanding of language. Yet when we turn to natural language, we encounter a huge and apparently messy collection of general terms; not...

Weak Quantifiers