Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics. Topically, mathematical logic bears close connections to metamathematics, the foundations of mathematics, and theoretical computer science. The unifying themes in mathematical logic include the study of the expressive power of formal systems and the deductive power of formal proof systems.
Mathematical logic is often divided into the fields of set theory, model theory, recursion theory, and proof theory. These areas share basic results on logic, particularly first-order logic, and definability. In computer science (particularly in the ACM Classification) mathematical logic encompasses additional topics not detailed in this article; see logic in computer science for those.
The Hebrew or Jewish calendar (הַלּוּחַ הָעִבְרִי, ha'luach ha'ivri) is a lunisolar calendar used today predominantly for Jewish religious observances. It determines the dates for Jewish holidays and the appropriate public reading of Torah portions, yahrzeits (dates to commemorate the death of a relative), and daily Psalm readings, among many ceremonial uses. In Israel, it is used for religious purposes, provides a time frame for agriculture and is an official calendar for civil purposes, although the latter usage has been steadily declining in favor of the Gregorian calendar.
The calendar used by Jews has evolved over time. The basic structural features of the early calendar are thought to have been influenced by the Babylonian calendar, including the seven-day week, the lunisolar intercalary adjustment and the names of the months. Until the Tannaitic period (approximately 10–220 CE) the calendar employed a new crescent moon, with an additional month normally added every two or three years to correct for the difference between twelve lunar months and the solar year. When to add it was based on observation of natural agriculture-related events. Through the Amoraic period (200–500 CE) and into the Geonic period, this system was gradually displaced by the mathematical rules used today. The principles and rules were fully codified by Maimonides in the Mishneh Torah in the 12th century. Maimonides' work also replaced counting "years since the destruction of the Temple" with the modern creation-era Anno Mundi.
A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year. If the solar year is defined as a tropical year, then a lunisolar calendar will give an indication of the season; if it is taken as a sidereal year, then the calendar will predict the constellation near which the full moon may occur. Usually there is an additional requirement that the year have a whole number of months, in which case most years have 12 months but every second or third year has 13.
The full moon cycle is a cycle of about 14 lunations over which full moons vary in apparent size and age (time since new moon). The sequence is