A System for Models of First Order Theories

If you want to know whether a property is true or not in a specific algebraic structure,you need to test that property on the given structure. This can be done by hand, which can be cumbersome and erroneous. In addition, the time consumed in testing depends on the size of the structure where the property is applied. We present an implementation of a system for finding counterexamples and testing properties of models of first-order theories. This system is supposed to provide a convenient and paperless environment for researchers and students investigating or studying such models and algebraic structures in particular. To implement a first-order theory in the system, a suitable first-order language.( and some axioms are required. The components of a language are given by a collection of variables, a set of predicate symbols, and a set of operation symbols. Variables and operation symbols are used to build terms. Terms, predicate symbols, and the usual logical connectives are used to build formulas. A first-order theory now consists of a language together with a set of closed formulas, i.e. formulas without free occurrences of variables. The set of formulas is also called the axioms of the theory. The system uses several different formats to allow the user to specify languages, to define axioms and theories and to create models. Besides the obvious operations and tests on these structures, we have introduced the notion of a functor between classes of models in order to generate more co~plex models from given ones automatically. As an example, we will use the system to create several lattices structures starting from a model of the theory of pre-orders.

The true history regarding alleged connection of the order of ancient, free and accepted Masons: with the abduction and murder of William Morgan in western New York, in 1826... (1886)

Cover title: Masonic light on the abduction and murder of Wm. Morgan.

Blue book for the use of subordinate divisions of the order of the Sons of Temperenance (1867)

Inscribed on front paste-down: Rothschild division No.227; and in pencil: James Jackson; and on front free endpaper: Presented to James M Clark By Mrs Amanda Burns Robert at Stayner 25 Aug. 1878.

Certificate of Acceptance and Initiation to Canadian Order Chosen Friends - Thomas Cowan

A certificate of initiation and acceptance to the Canadian Order Chosen Friends, Thomas Cowan. The certificate reads "This certifies that evidence has been received that Thomas Cowan has been accepted and initiated by the Council name below, and has thus become a member of the Canadian Order of Chosen Friends, and entitled to all the rights and privileges of membership and a benefit of not exceeding one thousand dollars from the relief fund of said order, which shall in case of death be paid to Annie Cowan his wife in the manner and subject to the conditions set forth in the laws governing said relief fund and in the application for membership. This certificate to be in force and binding when accepted in writing by the said member, with the acceptance attested by the Councilor and Recorder and the seal of the Subordinate Council affixed, so long as said member shall comply with the requirements of the Constitution, Laws and Regulations now in force or hereafter adopted for the government of the Order: otherwise, and also in the case of granting of a new certificate, to be null and void. In witness whereof, we have hereunto attached our signatures, and affixed the seal of the Grand Council of the Canadian Order of Chosen Friends. Dated the Twenty Seventh day of July, A.D. 1891." The front and back of the certificate are available for viewing.

Grand Lodge of Ontario Independent Order of Odd Fellows - William H. Cowan

A certificate from the Grand Lodge of Ontario Independent Order of Odd Fellows to brother William H. Cowan. He has been admitted as a member of Livingstone Lodge No. 130 at Merritton 19 October 1909. The certificate is signed and dated by W. Brooks (Secretary) and S.A. Poplestoise (Grand Master) December 7, 1911. Cowan received the Degree of Truth.

Order of Service for the Honour Roll Unveiling - 10 June, 1945

A dedication service program for those who gave their lives during World War II from the city of St. Catharines. The list of over 150 names was to be read aloud and an address made by the Mayor (W.J. Macdonald) with prayers and hymn to follow.

Order to create a General Board of Health in the Town of Niagara, June 25, 1832

In the early nineteenth century, a widespread outbreak of cholera occurred in continental Europe, eventually spreading to the British Isles. The disease subsequently spread to Canada as impoverished British immigrants seeking a better life arrived in the country. To help curb the spread of the disease, local Boards of Health were created.

Order to create a General Board of Health in the Town of Niagara, June 25, 1832.

In the early nineteenth century, a widespread outbreak of cholera occurred in continental Europe, eventually spreading to the British Isles. The disease subsequently spread to Canada as impoverished British immigrants seeking a better life arrived in the country. To help curb the spread of the disease, local Boards of Health were created.

Scottish Rite (Masonic Order) French Language Collection, 1787-1825, 1907, n.d.

The origins of the Scottish Rite of Freemasonry can be traced to France around 1754, when a Chapter of Claremont was founded in Paris. Initially this chapter had seven degrees, but by 1758 there were twenty-five degrees, known as the Rite of Perfection. In 1761, Stephen Morin was appointed to introduce the Rite into the New World. He began with Kingston, Jamaica and San Domingo. Further establishments were made in New Orleans, LA(1763); Albany, NY (1767); Philadelphia, PA (1782); and Charleston, SC (1783). In order to improve the disorganized state of the degrees in Europe, “Grand Constitutions” were enacted in 1786. These Constitutions formally brought into existence the “Ancient and Accepted Scottish Rite”. None of the degrees of the Scottish Rite would seem to have origins in Scotland. “Scottish” is translated from the French word “Ecossais”, which is found in some of the French titles of some of the degrees of the Rite of Perfection. It is possible that the Scottish connection is a result of the involvement of a Scotsman, Andrew Michael Ramsey, who may have devised some of the degrees.

Map - Probable Order of Battle

A map titled "Probable Order of Battle" and dated 28 May 1918. The map is of Montdidier.

The Order of Canada Investiture Ceremony Program (Selection of Pages)

A selection of pages from the program for the Order of Canada Investiture Ceremony in 2003 when Dorothy Wetherald Rungeling was a recipient.

Menu - Dinner on the occasion of the Investiture of the Order of Canada

A menu from the dinner of the Investiture of the Order of Canada.

Bulloch, Lade & Co. Order Form, 31 August 1870

An order form for the exportation of scotch pure malt whiskies, distilled by Bulloch, Lade & Co.

Proceedings of the Court Martial Held by Order of Major Merritt

Proceedings of the court martial held by order of Major Merritt (1 double-sided page, handwritten): Captain Hamilton gave evidence against Caleb Cook (a private in Major Merritt’s Company of Light Dragoons) for disobedience and leaving quarters without leave of absence. Cook was fined and ordered to spend one month in prison. The document is stained and has holes in it along the middle fold. This does not affect the text, Aug. 7, 1812.