# Ultraconstructive Model Theory via Bounded Adversarial Finite Structures

arXiv: https://arxiv.org/abs/2608.07534 · HTML: https://mlsanity.com/paper/2608.07534/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 11 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 2 of 2)

- [Logical GANs: Adversarial Learning through Ehrenfeucht Fraisse Games](https://mlsanity.com/paper/2510.22824/) (2025)
- [Model Theory of Ultrafinitism II: Deconstructing the Term Model (First Draft)](https://mlsanity.com/paper/2311.17931/) (2023)

## Abstract (arXiv)

Ultraconstructive Model Theory (UCMT) replaces idealized satisfaction, at finite compu- tational scale, by bounded adversarial survival. A finite partial structure is tested by an Opponent (Devil) drawing legal challenges from a bounded attack surface, repaired by a Builder (God) through legal replies, and certified by a symbolic Judge