# Anders Lundstedt: Natural induction—a model-theoretic study?

**Time: **
Wed 2022-03-30 10.00 - 12.00

**Location: **
Kräftriket, House 5, Room 31

**Lecturer: **
Anders Lundstedt (Stockholm University, Dept of Philosophy)

### Abstract

I present various notions of *inductiveness*—the original notion is due to Hetzl and Wong (2018). When suitably formulated, a *non-inductiveness* statement provides a precise and sensible sense in which a corresponding statement about the natural numbers is unprovable by straightforward induction. Thus by proving a suitable non-inductiveness result, one may show, in a precise and sensible manner sense, that some fact about the natural numbers is unprovable by straightforward induction.

I discuss the conceptual issue of how to formulate suitable non-inductiveness statements—where by ‘suitable’ I mainly mean formulations that actually provide the ‘sensible’ in my use of ‘precise and sensible sense’ above. Then I present techniques for proving non-inductiveness results: these are based on constructing certain kinds of non-standard models of first-order arithmetic.

I conclude by stating some non-inductiveness results that I have proved and some non-inductiveness conjectures that I hope to prove. If the conjectures turn out provable in the way I hope and believe, then that would perhaps justify removing the question mark from the ambitiously sounding paraphrase that is the title of this talk.

#### REFERENCES

- Hetzl, Stefan, and Tin Lok Wong (2018):
*Some observations on the logical foundations of inductive theorem proving*. In: Logical Methods in Computer Science**13**(4), pp. 1–26. (Corrected version of paper originally published Nov 16, 2017.)

My research page has some very outdated material. Perhaps some new material will appear there in time before the talk.