slideshow 3

Logic seminar

Not all Kripke models of HA are locally PA

Erfan Khaniki
IM CAS

 

Monday, 12. October 2020 - 16:00 to 17:30

Zoom meeting ID: 472 648 284 - https://cesnet.zoom.us/j/472648284

Let K be an arbitrary Kripke model of Heyting Arithmetic, HA. For every node k in K, we can view the classical structure of k, m_k, as a model of some classical theory of arithmetic. Let T be a classical theory in the language of arithmetic. We say K is locally T, iff for every k in K, m_k models T. A well-studied question in the model theory of HA is the following question: Is every Kripke model of HA locally PA? We answer this question negatively by constructing a Kripke model of HA which is not locally B\Sigma_1.