Does Not Force

The Mathematical Symbol "Does Not Force (⊮)"

Diving into the "Does Not Force" Symbol (⊮): A Journey through Model Theory

The mathematical universe is replete with symbols, each tailored to capture intricate concepts in a compact representation. In the context of model theory and certain areas of mathematical logic, the "Does Not Force" notation, denoted by ⊮, plays a pivotal role.

Deciphering the ⊮ Symbol

At its core, the ⊮ symbol is used to convey the non-forcibility of a particular statement within a given model or context. This becomes especially pertinent in areas like set theory, where forcing is a technique used to construct new models from existing ones, and the notion of a statement being "forced" (or not) in a model becomes crucial.

Example 1:

Let \( M \) be a model and \( \phi \) a statement. If \( \phi \) is not forced by the model \( M \), this relationship can be conveyed as:

\( M ⊮ \phi \)

Example 2:

Consider a scenario in forcing where we're working with a particular poset \( P \) and a condition \( p \). If \( p \) does not force a statement \( \psi \) to be true, this can be represented as:

\( p ⊮ \psi \)

Understanding the ⊮ notation is vital for mathematicians and logicians navigating the intricate terrains of model theory and set theory. The symbol serves as a stark reminder of the nuanced relationships that can exist between models and the statements or propositions they do or do not force.

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Codes for the ⊮ Symbol

The Symbol	⊮	copy
Alt Code	Alt 8878	copy
HTML Code	⊮	copy
HTML Entity	⊮	copy
CSS Code	\22AE	copy
Hex Code	⊮	copy
Unicode	U+22AE	copy

How To Insert the ⊮ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ⊮ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8878. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML Text	Output
<b>My symbol: &#8878;</b>	My symbol: ⊮

(Method 4) Use the HTML Entity Code (for webpages).

HTML Text	Output
<b>My symbol: &nVdash;</b>	My symbol: ⊮

(Method 5) Use the CSS Code (for webpages).

CSS and HTML Text	Output
<style> span:after { content: "\22AE";} </style> <span>My symbol:</span>	My symbol: ⊮

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML Text	Output
<b>My symbol: &#x22AE;</b>	My symbol: ⊮

On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22AE to place the ⊮ symbol on your canvas. For example:

JavaScript Text
const x = "0x"+"E9" ctx.fillText(String.fromCodePoint(x), 5, 5);
Output
⊮

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ⊮ is U+22AE. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:

Type	Output
22AE [Hold down Alt] [Press x]	⊮ (The 22AE turns into ⊮. Note that you can omit any leading zeros.)

In JavaScript, the syntax is \uXXXX. So, our example would be \u22AE. (Note that the format is 4 hexadecimal characters.)

JavaScript Text	Output
let str = "\u22AE" document.write("My symbol: " + str)	My symbol: ⊮

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