## Many sorted algebras (1994)

### Cached

### Download Links

Venue: | Journal of Formalized Mathematics |

Citations: | 130 - 14 self |

### BibTeX

@ARTICLE{Trybulec94manysorted,

author = {Andrzej Trybulec},

title = {Many sorted algebras},

journal = {Journal of Formalized Mathematics},

year = {1994},

volume = {6}

}

### Years of Citing Articles

### OpenURL

### Abstract

Summary. The basic purpose of the paper is to prepare preliminaries of the theory of many sorted algebras. The concept of the signature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between (1 sorted) universal algebras [8] and many sorted algebras with one sort only is described by introducing two functors mapping one into the other. The construction is done this way that the composition of both functors is the identity on universal algebras.

### Citations

1297 | Functions and their basic properties
- Byliński
- 1990
(Show Context)
Citation Context ...is done this way that the composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], [14], =-=[4]-=-, [5], [2], [9], [6], [7], [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition 1. P... |

1293 | Tarski Grothendieck set theory
- Trybulec
- 1990
(Show Context)
Citation Context ...other. The construction is done this way that the composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles =-=[10]-=-, [13], [12], [14], [4], [5], [2], [9], [6], [7], [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the fol... |

1229 | Properties of subsets
- Trybulec
- 1990
(Show Context)
Citation Context ... The construction is done this way that the composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], =-=[13]-=-, [12], [14], [4], [5], [2], [9], [6], [7], [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following... |

1049 | Functions from a set to a set
- Byliński
- 1990
(Show Context)
Citation Context ...ne this way that the composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], [14], [4], =-=[5]-=-, [2], [9], [6], [7], [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition 1. PRELIM... |

1024 | Relations and their basic properties
- Woronowicz
- 1990
(Show Context)
Citation Context ...ction is done this way that the composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], =-=[14]-=-, [4], [5], [2], [9], [6], [7], [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition... |

463 | Partial functions
- Byliński
- 1990
(Show Context)
Citation Context ...t the composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], [14], [4], [5], [2], [9], =-=[6]-=-, [7], [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition 1. PRELIMINARIES (1) It ... |

370 |
Subsets of real numbers
- Trybulec
(Show Context)
Citation Context ...onstruction is done this way that the composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], =-=[12]-=-, [14], [4], [5], [2], [9], [6], [7], [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following propo... |

315 | Finite sequences and tuples of elements of a non-empty sets
- Byliński
- 1990
(Show Context)
Citation Context ... composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], [14], [4], [5], [2], [9], [6], =-=[7]-=-, [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition 1. PRELIMINARIES (1) It is no... |

280 | Binary operations applied to functions
- Trybulec
- 1990
(Show Context)
Citation Context ...y that the composition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], [14], [4], [5], [2], =-=[9]-=-, [6], [7], [1], [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition 1. PRELIMINARIES (1... |

267 | Pigeon hole principle
- Trybulec
- 1990
(Show Context)
Citation Context ...construction is done this way that the composition of both functors is the identity on universal algebras. MML Identifier: MSUALG 1. The articles [12], [14], [5], [6], [2], [10], [7], [4], [1], [11], =-=[13]-=-, [3], [8], and [9] provide the notation and terminology for this paper. 1. Preliminaries In this paper i, j are arbitrary and I is a set. Next we state the proposition (1) It is not true that there e... |

240 | König’s theorem
- Bancerek
- 1990
(Show Context)
Citation Context ...osition of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], [14], [4], [5], [2], [9], [6], [7], =-=[1]-=-, [11], [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition 1. PRELIMINARIES (1) It is not tru... |

198 | Many-sorted sets
- Trybulec
- 1993
(Show Context)
Citation Context ...on of both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], [14], [4], [5], [2], [9], [6], [7], [1], =-=[11]-=-, [3], and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition 1. PRELIMINARIES (1) It is not true that... |

96 | Group and field definitions
- Białas
- 1990
(Show Context)
Citation Context ...both functors is the identity on universal algebras. MML Identifier:MSUALG_1. WWW:http://mizar.org/JFM/Vol6/msualg_1.html The articles [10], [13], [12], [14], [4], [5], [2], [9], [6], [7], [1], [11], =-=[3]-=-, and [8] provide the notation and terminology for this paper. In this paper i, j denote sets and I denotes a set. One can prove the following proposition 1. PRELIMINARIES (1) It is not true that ther... |

51 |
Group and field definitions
- Bialas
- 1990
(Show Context)
Citation Context ...uction is done this way that the composition of both functors is the identity on universal algebras. MML Identifier: MSUALG 1. The articles [12], [14], [5], [6], [2], [10], [7], [4], [1], [11], [13], =-=[3]-=-, [8], and [9] provide the notation and terminology for this paper. 1. Preliminaries In this paper i, j are arbitrary and I is a set. Next we state the proposition (1) It is not true that there exists... |

32 |
Małgorzata Korolkiewicz. Basic notation of universal algebra
- Kotowicz, Madras
- 1992
(Show Context)
Citation Context ...ature of a many sorted algebra is introduced as well as the concept of many sorted algebra itself. Some auxiliary related notions are defined. The correspondence between (1 sorted) universal algebras =-=[8]-=- and many sorted algebras with one sort only is described by introducing two functors mapping one into the other. The construction is done this way that the composition of both functors is the identit... |

15 | Maximal discrete subspaces of almost discrete topological spaces
- Karno
- 1993
(Show Context)
Citation Context ...n is done this way that the composition of both functors is the identity on universal algebras. MML Identifier: MSUALG 1. The articles [12], [14], [5], [6], [2], [10], [7], [4], [1], [11], [13], [3], =-=[8]-=-, and [9] provide the notation and terminology for this paper. 1. Preliminaries In this paper i, j are arbitrary and I is a set. Next we state the proposition (1) It is not true that there exists a no... |