Journal of Formalized Mathematics
Volume 9, 1997
University of Bialystok
Copyright (c) 1997 Association of Mizar Users

## Equations in Many Sorted Algebras

Artur Kornilowicz
Warsaw University, Bialystok

### Summary.

This paper is preparation to prove Birkhoff's Theorem. Some properties of many sorted algebras are proved. The last section of this work shows that every equation valid in a many sorted algebra is also valid in each subalgebra, and each image of it. Moreover for a family of many sorted algebras $(A_i: i \in I)$ if every equation is valid in each $A_i$, $i \in I$ then is also valid in product $\prod(A_i: i \in I)$.

#### MML Identifier: EQUATION

The terminology and notation used in this paper have been introduced in the following articles [20] [8] [25] [24] [26] [5] [7] [6] [21] [10] [3] [9] [1] [22] [23] [15] [16] [17] [4] [13] [14] [12] [19] [18] [11] [2]

#### Contents (PDF format)

1. On the Functions and Many Sorted Functions
2. On the Many Sorted Algebras
3. Equations in Many Sorted Algebras

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