## Journal of Symbolic Logic

### Free Set Algebras Satisfying Systems of Equations

G. Aldo Antonelli

#### Abstract

In this paper we introduce the notion of a set algebra $\mathscr{S}$ satisfying a system $\mathscr{E}$ equations. After defining a notion of freeness for such algebras, we show that, for any system $\mathscr{E}$ of equations, set algebras that are free in the class of structures satisfying $\mathscr{E}$ exist and are unique up to a bisimulation. Along the way, analogues of classical set-theoretic and algebraic properties are investigated.

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 4 (1999), 1656-1674.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745945

Mathematical Reviews number (MathSciNet)
MR1780077

Zentralblatt MATH identifier
0952.03044

JSTOR