Martin's maximum

In set theory, a branch of mathematical logic, Martin's maximum, introduced by Foreman, Magidor & Shelah (1988), is a generalization of the proper forcing axiom, itself a generalization of Martin's axiom. It represents the broadest class of forcings for which a forcing axiom is consistent.

Martin's maximum (MM) states that if D is a collection of dense subsets of a notion of forcing that preserves stationary subsets of ω₁, then there is a D-generic filter. It is a well known fact that forcing with a ccc notion of forcing preserves stationary subsets of ω₁, thus MM extends MA(). If (P,≤) is not a stationary set preserving notion of forcing, i.e., there is a stationary subset of ω₁, which becomes nonstationary when forcing with (P,≤), then there is a collection D of dense subsets of (P,≤), such that there is no D-generic filter. This is why MM is called the maximal extension of Martin's axiom.

The existence of a supercompact cardinal implies the consistency of Martin's maximum. The proof uses Shelah's theories of semiproper forcing and iteration with revised countable supports.

Martin's

Martin's may refer to:

Retailers

Martin's (New York)

Martin's was a specialty apparel retailer in the New York metropolitan area, with its flagship location on Fulton Street in Brooklyn. It grew to six stores by the mid 1970s, before being sold to the operator of Times Square Stores in 1977.

History

A Store Grows In Brooklyn

The history of Martin's dates back to at least 1903. Hyman Zeitz (c. 1860-1930), who emigrated to the United States in 1882, opened a coat and suit department in an existing blouse shop called Martin's at the corner of Fulton and Bridge Street in Brooklyn, New York. He eventually bought out the owner. The business gradually expanded, and in 1924 moved next door into the seven-story Offerman Building. In 1930, Hyman Zeitz died, and his son Fred. J. Zeitz took over as president (a position he held for over 35 years).

In 1947, a modernized entrance to the Offerman Building, designed by architect Morris Lapidus, was completed, replacing the "gimcracks of the victorian era" with modern "simplicity."

Suburban Expansion

RS McColl

RS McColl, or "McColl's" is a Scottish newsagent company named after Robert Smyth McColl, who was a professional footballer. It was founded in 1901 by McColl and his brother Tom.

RS McColl is a trading name of McColls Retail Group, It has been a prominent Scottish confectioner and newsagent and has been owned in the past by Cadburys and the Southland Corporation of America (7-Eleven).

Business background and history

In 1998 RS McColl became part of TM Retail when Forbuoys (a subsidiary of TM Retail) acquired Martin Retail Group, creating Great Britain's largest chain of newsagents. In addition to RS McColl, TM Retail's other trading names include; Forbuoys, Martin's, Dillons (purchased from One Stop Stores Ltd following the takeover by Tesco of parent company T&S Stores),McColls and More.

In 2006 TM Retail was renamed Martin McColl Limited after a management buyout. The various stores were then rebranded variously as Martin's (news and variety stores) or McColl's (convenience stores). The only exceptions were the Scottish stores where the RS McColl name was retained. With this re-branding all other names the company operates under were removed, these included Martins the Newsagents, More, Forbuoys and Dillons.