Fusion over sublanguages

Assaf Hasson; Martin Hils

doi:10.2178/jsl/1146620149

Fusion over sublanguages

Assaf Hasson, Martin Hils

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Generalising Hrushovski's fusion technique we construct the free fusion of two strongly minimal theories T₁, T₂ intersecting in a totally categorical sub-theory T₀. We show that if, e.g., T ₀ is the theory of infinite vector spaces over a finite field then the fusion theory T_ω exists, is complete and ω-stable of rank ω. We give a detailed geometrical analysis of T_ω, proving that if both T₁, T₂ are 1-based then. T _ω can be collapsed into a strongly minimal theory, if some additional technical conditions hold - all trivially satisfied if T₀ is the theory of infinite vector spaces over a finite field F₄.

Original language	English
Pages (from-to)	361-398
Number of pages	38
Journal	Journal of Symbolic Logic
Volume	71
Issue number	2
DOIs	https://doi.org/10.2178/jsl/1146620149
State	Published - 1 Jun 2006
Externally published	Yes

ASJC Scopus subject areas

Philosophy
Logic

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AB - Generalising Hrushovski's fusion technique we construct the free fusion of two strongly minimal theories T1, T2 intersecting in a totally categorical sub-theory T0. We show that if, e.g., T 0 is the theory of infinite vector spaces over a finite field then the fusion theory Tω exists, is complete and ω-stable of rank ω. We give a detailed geometrical analysis of Tω, proving that if both T1, T2 are 1-based then. T ω can be collapsed into a strongly minimal theory, if some additional technical conditions hold - all trivially satisfied if T0 is the theory of infinite vector spaces over a finite field F4.

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Fusion over sublanguages

Abstract

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