Albert Visser
University of Utrecht
Introduction to Interpretations
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Lecture 1: Basics
Lecture 2: Categories and Sameness
Lecture 3: The Interpretation Existence Lemma
Lecture 4: The Smullyan Bootstrap

There could be many introductions to interpretations, so the tutorial will, in some measure, reflect my personal interests. We discuss two connected questions. When are two interpretations the same? When are two theories the same? We illustrate how different notions of sameness of interpretation lead to different notions of sameness of theory. A central result of logic is the Model Existence Lemma. We show how this result has a theory-internal shadow: the Interpretation Existence Lemma. Roughly, if theory T proves the consistency of theory U, then T interprets U. We consider some applications of this fundamental result. We enrich theories for various applications like the incompleteness theorems. A bootstrap for enrichment often takes the form of a series of interpretations. We illustrate this methodology by zooming in on a specific bootstrap that is aimed at adding sequences to a theory. The first step of our bootstrap is the Smullyan interpretation of binary strings. The second step builds sequences from strings.

Mateusz Łełyk
University of Warsaw
TBA
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TBA

Isabel Oitavem
Universidade Nova de Lisboa
TBA
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TBA

(Tentative) Schedule for Both Days (8-9 October 2026)

• 10:15–11:00 – Albert Visser
• 11:00–11:30 – Coffee Break
• 11:30–12:15 – Albert Visser
• 12:15–13:30 – Lunch
• 13:30–14:15 – Mateusz Łełyk
• 14:15–14:25 – Short Break
• 14:25–15:10 – Mateusz Łełyk
• 15:10–15:40 – Coffee Break
• 15:40–16:25 – Isabel Oitavem
• 16:25–16:30 – Short Break
• 16:30–17:15 – Isabel Oitavem

The workshop is free of charge and open to all interested participants. No registration is required to attend the workshop.

This workshop is preceded by the workshop Metamathematical Miscellanea which will take place in Lugano the 5th and 6th October. Anyone is welcome to attend this workshop as well. For more information, please consult this website.