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Keith Kearnes
Keith Kearnes
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Here are some papers.

(1)
Baldwin, J. T.; Shelah, S.
The structure of saturated free algebras.
Algebra Universalis 17 (1983), no. 2, 191-199.

From the Math Review (written by Steve Comer):

The authors investigate the structure of an algebra $M$ in a variety $V$ (with a countable similarity type) such that $M$ is free and ℵ1-saturated. The main result says that "every model of Th($M$) is `generated' by the union of a finite set of indiscernible sequences.

(2)

Belegradek, O. V.
Model theory for locally free algebras.
Trudy Inst. Mat. (Novosibirsk) 8 (1988), Teor. Model. i ee Primenen., 3-25, 184.

From the abstract:

In this paper we study model-theoretic properties of locally free algebras. It is proved that every complete theory of locally free algebras is stable and normal.

(23)
Mekler, Alan H.; Shelah, Saharon
Almost free algebras.
Israel J. Math. 89 (1995), no. 1-3, 237-259.

From the Math Review (written by John Baldwin):

An algebra $A$ is "almost free'' if most of its subalgebras of smaller cardinality are free. A is essentially free if the free product of $A$ and $F$ is free for some free algebra $F$; otherwise, $A$ is essentially non-free. The authors characterize the class of cardinals in which a variety $V$ has an essentially non-free algebra which is almost free.

(3)
Baldwin, J. T.; Shelah, S.
The structure of saturated free algebras.
Algebra Universalis 17 (1983), no. 2, 191-199.

From the Math Review (written by Steve Comer):

The authors investigate the structure of an algebra $M$ in a variety $V$ (with a countable similarity type) such that $M$ is free and ℵ1-saturated. The main result says that "every model of Th($M$) is `generated' by the union of a finite set of indiscernible sequences.

 

More recently,

(4)
Kucera, Thomas G.; Pillay, Anand
Saturated free algebras and almost indiscernible theories.
Algebra Universalis 83 (2022), no. 1, Paper No. 11, 25 pp.

This is a very recent paper and the Math Review is not yet posted. But Kucera spoke about this in our seminar last month and you will find links to slides and video for his talk at the foot of the page for the abstract of his talk.

Here are some papers.

(1)
Belegradek, O. V.
Model theory for locally free algebras.
Trudy Inst. Mat. (Novosibirsk) 8 (1988), Teor. Model. i ee Primenen., 3-25, 184.

From the abstract:

In this paper we study model-theoretic properties of locally free algebras. It is proved that every complete theory of locally free algebras is stable and normal.

(2)
Mekler, Alan H.; Shelah, Saharon
Almost free algebras.
Israel J. Math. 89 (1995), no. 1-3, 237-259.

From the Math Review (written by John Baldwin):

An algebra $A$ is "almost free'' if most of its subalgebras of smaller cardinality are free. A is essentially free if the free product of $A$ and $F$ is free for some free algebra $F$; otherwise, $A$ is essentially non-free. The authors characterize the class of cardinals in which a variety $V$ has an essentially non-free algebra which is almost free.

(3)
Baldwin, J. T.; Shelah, S.
The structure of saturated free algebras.
Algebra Universalis 17 (1983), no. 2, 191-199.

From the Math Review (written by Steve Comer):

The authors investigate the structure of an algebra $M$ in a variety $V$ (with a countable similarity type) such that $M$ is free and ℵ1-saturated. The main result says that "every model of Th($M$) is `generated' by the union of a finite set of indiscernible sequences.

 

More recently,

(4)
Kucera, Thomas G.; Pillay, Anand
Saturated free algebras and almost indiscernible theories.
Algebra Universalis 83 (2022), no. 1, Paper No. 11, 25 pp.

This is a very recent paper and the Math Review is not yet posted. But Kucera spoke about this in our seminar last month and you will find links to slides and video for his talk at the foot of the page for the abstract of his talk.

Here are some papers.

(1)
Baldwin, J. T.; Shelah, S.
The structure of saturated free algebras.
Algebra Universalis 17 (1983), no. 2, 191-199.

From the Math Review (written by Steve Comer):

The authors investigate the structure of an algebra $M$ in a variety $V$ (with a countable similarity type) such that $M$ is free and ℵ1-saturated. The main result says that "every model of Th($M$) is `generated' by the union of a finite set of indiscernible sequences.

(2)

Belegradek, O. V.
Model theory for locally free algebras.
Trudy Inst. Mat. (Novosibirsk) 8 (1988), Teor. Model. i ee Primenen., 3-25, 184.

From the abstract:

In this paper we study model-theoretic properties of locally free algebras. It is proved that every complete theory of locally free algebras is stable and normal.

(3)
Mekler, Alan H.; Shelah, Saharon
Almost free algebras.
Israel J. Math. 89 (1995), no. 1-3, 237-259.

From the Math Review (written by John Baldwin):

An algebra $A$ is "almost free'' if most of its subalgebras of smaller cardinality are free. A is essentially free if the free product of $A$ and $F$ is free for some free algebra $F$; otherwise, $A$ is essentially non-free. The authors characterize the class of cardinals in which a variety $V$ has an essentially non-free algebra which is almost free.

More recently,

(4)
Kucera, Thomas G.; Pillay, Anand
Saturated free algebras and almost indiscernible theories.
Algebra Universalis 83 (2022), no. 1, Paper No. 11, 25 pp.

This is a very recent paper and the Math Review is not yet posted. But Kucera spoke about this in our seminar last month and you will find links to slides and video for his talk at the foot of the page for the abstract of his talk.

Source Link
Keith Kearnes
Keith Kearnes
  • 14.6k
  • 2
  • 50
  • 86

Here are some papers.

(1)
Belegradek, O. V.
Model theory for locally free algebras.
Trudy Inst. Mat. (Novosibirsk) 8 (1988), Teor. Model. i ee Primenen., 3-25, 184.

From the abstract:

In this paper we study model-theoretic properties of locally free algebras. It is proved that every complete theory of locally free algebras is stable and normal.

(2)
Mekler, Alan H.; Shelah, Saharon
Almost free algebras.
Israel J. Math. 89 (1995), no. 1-3, 237-259.

From the Math Review (written by John Baldwin):

An algebra $A$ is "almost free'' if most of its subalgebras of smaller cardinality are free. A is essentially free if the free product of $A$ and $F$ is free for some free algebra $F$; otherwise, $A$ is essentially non-free. The authors characterize the class of cardinals in which a variety $V$ has an essentially non-free algebra which is almost free.

(3)
Baldwin, J. T.; Shelah, S.
The structure of saturated free algebras.
Algebra Universalis 17 (1983), no. 2, 191-199.

From the Math Review (written by Steve Comer):

The authors investigate the structure of an algebra $M$ in a variety $V$ (with a countable similarity type) such that $M$ is free and ℵ1-saturated. The main result says that "every model of Th($M$) is `generated' by the union of a finite set of indiscernible sequences.

More recently,

(4)
Kucera, Thomas G.; Pillay, Anand
Saturated free algebras and almost indiscernible theories.
Algebra Universalis 83 (2022), no. 1, Paper No. 11, 25 pp.

This is a very recent paper and the Math Review is not yet posted. But Kucera spoke about this in our seminar last month and you will find links to slides and video for his talk at the foot of the page for the abstract of his talk.