Omega-models in analytical hierarchy
Krzysztof Rafal Apt · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1972
We consider co-models of the second order arithmetic A2 , which are the subsets of the class of analytical sets.It is proved that there exist w-models of A2 'l{, such that'll r. u1: u Il>= =LI~ and 'll u (JI~ u L'~) ~ Lli, and that there are no OJ-models which lie lower in the analytical hierarchy.It is shown that there exist ro-models of A2 in which every set is analytical but no code is analytical.Finally, we prove some results concerning hyperdegrees, e.g. the existence of "many" uncountable antichains of hyperdegrees.