5 Rigid solvable groups. Algebraic geometry and model theory
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Nikolay Romanovskii
Abstract
We give a survey of the papers of the author and A. Miasnikov on rigid solvable groups. We highlight the following results: equationally Noetherian property of rigid groups is proved, dimension theory for rigid groups is constructed, the formulation of the Hilbert’s Nullstellensatz for rigid groups is found and this theorem is proved, the completeness and ω-stability of the theory of divisible m-rigid groups is proved, saturated models are described.
Abstract
We give a survey of the papers of the author and A. Miasnikov on rigid solvable groups. We highlight the following results: equationally Noetherian property of rigid groups is proved, dimension theory for rigid groups is constructed, the formulation of the Hilbert’s Nullstellensatz for rigid groups is found and this theorem is proved, the completeness and ω-stability of the theory of divisible m-rigid groups is proved, saturated models are described.
Chapters in this book
- Frontmatter I
- Introduction V
- Contents IX
- 1 Model theory and groups 1
- 2 Independence and interpretable structures in nonabelian free groups 51
- 3 Quantifier elimination algorithm to boolean combination of ∃∀-formulas in the theory of a free group 87
- 4 Rich groups, weak second-order logic, and applications 127
- 5 Rigid solvable groups. Algebraic geometry and model theory 193
- Index 231
Chapters in this book
- Frontmatter I
- Introduction V
- Contents IX
- 1 Model theory and groups 1
- 2 Independence and interpretable structures in nonabelian free groups 51
- 3 Quantifier elimination algorithm to boolean combination of ∃∀-formulas in the theory of a free group 87
- 4 Rich groups, weak second-order logic, and applications 127
- 5 Rigid solvable groups. Algebraic geometry and model theory 193
- Index 231
